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A Kriging-based constrained global optimization algorithm for expensive black-box functions with infeasible initial points

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Abstract

In many engineering optimization problems, the objective and the constraints which come from complex analytical models are often black-box functions with extensive computational effort. In this case, it is necessary for optimization process to use sampling data to fit surrogate models so as to reduce the number of objective and constraint evaluations as soon as possible. In addition, it is sometimes difficult for the constrained optimization problems based on surrogate models to find a feasible point, which is the premise of further searching for a global optimal feasible solution. For this purpose, a new Kriging-based Constrained Global Optimization (KCGO) algorithm is proposed. Unlike previous Kriging-based methods, this algorithm can dispose black-box constrained optimization problem even if all initial sampling points are infeasible. There are two pivotal phases in KCGO algorithm. The main task of the first phase is to find a feasible point when there is no feasible data in the initial sample. And the aim of the second phase is to obtain a better feasible point under the circumstances of fewer expensive function evaluations. Several numerical problems and three design problems are tested to illustrate the feasibility, stability and effectiveness of the proposed method.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Nos. 51575205 and 61370182), the Program for Science & technology Innovation teams in Universities of Henan Province (No. 14IRTSTHN022) and Henan Natural Science Foundation (No. 162300410263).

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Authors and Affiliations

  1. National CAD Supported Software Engineering Centre, Huazhong University of Science and Technology, Wuhan, 430074, People’s Republic of China

    Yaohui Li, Yizhong Wu, Jianjun Zhao & Liping Chen

  2. School of Mechano-Electronic Engineering, Xuchang University, Xuchang, 461000, Henan, China

    Yaohui Li

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  1. Yaohui Li
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  2. Yizhong Wu
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  3. Jianjun Zhao
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  4. Liping Chen
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Correspondence to Yizhong Wu.

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Li, Y., Wu, Y., Zhao, J. et al. A Kriging-based constrained global optimization algorithm for expensive black-box functions with infeasible initial points. J Glob Optim 67, 343–366 (2017). https://doi.org/10.1007/s10898-016-0455-z

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  • DOI: https://doi.org/10.1007/s10898-016-0455-z

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